On the basis of the dynamic version of linear Donnell type equations and with deformations before instability taken into account, the dynamic instability of simply supported, functionally graded (FG) truncated conical shells under static and time dependent periodic axial loads is analyzed. Appling Galerkin's method, the partial differential equations are reduced into a Mathieu-type differential equation describing the dynamic instability behavior of the FG conical shell. The domains of principal instability are determined by using Bolotin's method. Validation of numerical results was done with those available from previous researches. The influences of various parameters like static and dynamic load factors, volume fraction index, FG profiles and shell characteristics on the domains of dynamic instability of conical shell were investigated. (C) 2015 Elsevier Ltd. All rights reserved.